Thanks for sending your question. The name you mentioned means "flag"/"emblem"/"banner", anything that represents a cause or group. It is the name of Raiyah bint al-Hussain, daughter of King Hussain of Jordan. The name is not pronounced like "rear", it is pronounced [(RA)ndom] + [(YU)mmy], with emphasis on Ra, i.e. like Raa-yuh.
Raiyah is an acceptable name for a Muslim baby. It is not from a Quranic root, but this is not a problem, for example the common name Zaynab is not from a Quranic root either.
Raiyah Rahman means "Rahman's banner", i.e. God's banner. It means that the girl represents God's cause.
Akhtar means "celestial object", anything bright you see in the sky, thus it means "star", "planet".
Raiyah Rahman Akhtar is an acceptable name. Some scholars do not recommend using names that contain tazkiyah, which is any name that suggests the baby is a pious person, and Raiyah Rahman does contain a little of that. For this reason it might be better to change Rahman to something else. Rahmah would work ("mercy").